I need help finding and stating the domains of two different functions in interval notation.
f(x) = x^4 / x^2+x-6
I'm pretty sure that this one is all negative numbers up to 3 and all numbers greater than 2, but 0 also seems to fit. How would I state the domain in interval notation, though?
g(x) = (√x) / 2x^2+x-1
I don't know how to find the domain of this one at all, except that x cannot be a negative number.
Help and explanations would be greatly appreciated!
f(x) = x^4 / x^2+x-6
I'm pretty sure that this one is all negative numbers up to 3 and all numbers greater than 2, but 0 also seems to fit. How would I state the domain in interval notation, though?
g(x) = (√x) / 2x^2+x-1
I don't know how to find the domain of this one at all, except that x cannot be a negative number.
Help and explanations would be greatly appreciated!
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For the first one, you're pretty close. However, the only points that don't work are -3 and 2, which is what you found. However, all the points between those work, like 0. So the domain would be:
(negative infinity, -3), (-3, 2), (2, infinity)
For the second one, you're absolutely correct that x can't be less than zero. Now you have find where the bottom is zero, which would make g(x) undefined. The bottom factors as (2x-1)(x+1). So now we have asymptotes at x = .5 and x = -1. But wait, the function never goes left pass x = 0, so there is no asymptote at x = -1. So the only asymptote is @ x = .5 So the domain is:
[0, .5), (.5, infinity)
(negative infinity, -3), (-3, 2), (2, infinity)
For the second one, you're absolutely correct that x can't be less than zero. Now you have find where the bottom is zero, which would make g(x) undefined. The bottom factors as (2x-1)(x+1). So now we have asymptotes at x = .5 and x = -1. But wait, the function never goes left pass x = 0, so there is no asymptote at x = -1. So the only asymptote is @ x = .5 So the domain is:
[0, .5), (.5, infinity)